<p>\(ABCD\) is a square of sides \((x + 1)\) cm. \(XYZ\) is a right-angled triangle where angle \(XYZ\) is \(90^\circ\), \(XY = (2x + 5)\) cm and \(YZ = (2x - 1)\) cm.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Given that the area of triangle \(XYZ\) is \(1.5\) times the area of the square \(ABCD\), form an equation, in terms of \(x\), and show that it reduces to \(x^2 + 2x - 8 = 0\).</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Solve the equation in part <strong>(a)</strong> by factorisation and find the perimeter of the square \(ABCD\).<span class="inline-marks">[3]</span></div></li></ol>

\(ABCD\) is a square of sides \((x + 1)\) cm. \(XYZ\) is a right-angled triangle where angle \(XYZ\) is \(90^\circ\), \(XY = (2x + 5)\) cm and \(YZ = (2x - 1)\) cm.

Given that the area of triangle \(XYZ\) is \(1.5\) times the area of the square \(ABCD\), form an equation, in terms of \(x\), and show that it reduces to \(x^2 + 2x - 8 = 0\).

Solve the equation in part **(a)** by factorisation and find the perimeter of the square \(ABCD\).